Plz Answer..... ♥ ♥ ☺..
A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
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Answers
Answer:
Given:- Circular park with radius 20m.
Let Ankur Syed and David be donated by points A,S&D respectively. Given all there are sitting at equal distance i.e AS=SD=AD
To find: Length of AS=SD=AD
Explanation: LEt AS=SD=AD=2x [Ref. image 1]
In ASD, all sides are equal,
∴ASD is equilateral triangle
We draw OP⊥SD (perpendicular drawn from centre of circle to a chord of the chord)
So, SP=DP=
2
1
SD [Ref. image 2]
⇒SP=DP=
2
2x
=x
Join OS & AO
In ΔOPS
By Pythagoras theorem
OS
2
=OP
2
+PS
2
(20)
2
=OP
2
+x
2
(400)=OP+x
2
400−x
2
=OP
2
OP=
400−x
2
In △APS
By Pythagoras theorem
AS
2
=AP
2
+PS
2
(2x)
2
=AP
2
+x
2
$$4x^2 = AP^2+x^2
4x
2
−x
2
=AP
2
3x
2
=AP
2
AP=
3x
Now
AP=AO+OP (Medium of equilateral triangle passes through its circum center)
3
x=20+
400−x
2
[Ref. image 3]
3
x−20=
400−x
2
400−x
2
=
3
x−20
Squaring on both sides
(
400−x
2
)
2
=(
3
x−20)
2
400−x
2
=(3x
2
+(20)×20−2×(
3
x)×20
⇒400−x
2
=3x
2
+400−40
3
x
⇒400−400+40
3
x=3x
2
+x
⇒40
3
x=4x
2
⇒4x
2
=40
3
x
⇒
x
x
2
=
4
40
3
⇒x=10
3
m
Step-by-step explanation:
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